Solve for $x$ :
\[
\begin{array}{l}
6^{8 x-4}=5^{3 x-4} \\
x=
\end{array}
\]

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Answer

$\boxed{x = \frac{4\ln(5) + 4\ln(6)}{8\ln(6) - 3\ln(5)}}$

Steps

Step 1 ：$\ln(6^{8x-4}) = \ln(5^{3x-4})$

Step 2 ：$(8x-4)\ln(6) = (3x-4)\ln(5)$

Step 3 ：$8x\ln(6) - 4\ln(6) = 3x\ln(5) - 4\ln(5)$

Step 4 ：$8x\ln(6) - 3x\ln(5) = 4\ln(5) + 4\ln(6)$

Step 5 ：$x(8\ln(6) - 3\ln(5)) = 4\ln(5) + 4\ln(6)$

Step 6 ：$x = \frac{4\ln(5) + 4\ln(6)}{8\ln(6) - 3\ln(5)}$

Step 7 ：$\boxed{x = \frac{4\ln(5) + 4\ln(6)}{8\ln(6) - 3\ln(5)}}$